Question

what is the sum of the angle measures in a linear pair?
what is the sum of all the angle measures in the diagram?
(m∠1 + m∠4) + (m∠2 + m∠5) + (m∠3 + m∠6) =
(m∠1 + m∠4) + (m∠2 + m∠5) + (m∠3 + m∠6)
180° + 180° + 180°

Explanation:

Step1: Analyze the number of linear pairs

There are 3 linear pairs in the diagram: \((\angle1,\angle4)\), \((\angle2,\angle5)\), \((\angle3,\angle6)\)

Step2: Use the property of linear pairs

The sum of measures of angles in a linear pair is \(180^{\circ}\).
So \((m\angle1 + m\angle4)+(m\angle2 + m\angle5)+(m\angle3 + m\angle6)=180^{\circ}+180^{\circ}+180^{\circ}\)

Answer:

\(540^{\circ}\)